Market concentration

In economics, market concentration is a function of the number of firms and their respective shares of the total production (alternatively, total capacity or total reserves) in a market. Alternative terms are Industry concentration and Seller concentration.[1]

Market concentration is related to industrial concentration, which concerns the distribution of production within an industry, as opposed to a market. In industrial organization, market concentration may be used as a measure of competition, theorized to be positively related to the rate of profit in the industry, for example in the work of Joe S. Bain.

When antitrust agencies are evaluating a potential violation of competition laws, they will typically make a determination of the relevant market and attempt to measure market concentration within the relevant market.

Empirical studies that are designed to test the relationship between market concentration and prices are collectively known as price-concentration studies; see Weiss (1989).

Typically, any study that claims to test the relationship between price and the level of market concentration is also (jointly, that is, simultaneously) testing whether the market definition (according to which market concentration is being calculated) is relevant; that is, whether the boundaries of each market is not being determined either too narrowly or too broadly so as to make the defined "market" meaningless from the point of the competitive interactions of the firms that it includes (or is made of).

In economics, market concentration is a criterion that can be used to rank order various distributions of firms' shares of the total production (alternatively, total capacity or total reserves) in a market.

A simple measure of market concentration is 1/N where N is the number of firms in the market. This measure of concentration ignores the dispersion among the firms' shares. It is decreasing in the number of firms and nonincreasing in the degree of symmetry between them. This measure is practically useful only if a sample of firms' market shares is believed to be random, rather than determined by the firms' inherent characteristics.

CCI=s1+∑i=2Nsi2(2−si){\displaystyle CCI=s_{1}+\sum _{i=2}^{N}s_{i}^{2}(2-s_{i})} where s1 is the share of the largest firm. The index is similar to 2H−∑si3{\displaystyle 2{\text{H}}-\sum s_{i}^{3}} except that greater weight is assigned to the share of the largest firm.

(d) The Pareto slope (Ijiri and Simon, 1971). If the Pareto distribution is plotted on double logarithmic scales, [then] the distribution function is linear, and its slope can be calculated if it is fitted to an observed size-distribution.

(e) The Linda index (1976)

L=1N(N−1)∑i=1N−1Qi{\displaystyle L={\frac {1}{N(N-1)}}\sum _{i=1}^{N-1}Q_{i}} where Qi is the ratio between the average share of the first i{\displaystyle i} firms and the average share of the remaining N−i{\displaystyle N-i} firms. This index is designed to measure the degree of inequality between values of the size variable accounted for by various sub-samples of firms. It is also intended to define the boundary between the oligopolists within an industry and other firms. It has been used by the European Union.

(f) The U Index (Davies, 1980):

U=I∗aN−1{\displaystyle U=I^{*a}N^{-1}} where I∗{\displaystyle I^{*}} is an accepted measure of inequality (in practice the coefficient of variation is suggested), a{\displaystyle a} is a constant or a parameter (to be estimated empirically) and N is the number of firms. Davies (1979) suggests that a concentration index should in general depend on both N and the inequality of firms' shares.

The "number of effective competitors" is the inverse of the Herfindahl index.

Terrence Kavyu Muthoka defines distribution just as functionals in the Swartz space which is the space of functions with compact support and with all derivatives existing.The Media:Dirac Distribution or the Dirac function is a good example .